Question

A solution of urea (mol mass $56\, g\, mol^{-1})$ boils at $100.18 ^\circ\,C$ at the atmospheric pressure. If $K_f$ and $K_b$ for water are $1.86$ and $0.512\, K\, kg$ $mol^{-1}$ the above solution will freeze at

• A. -6.54$^\circ$C
• B. 6.54$^\circ$C
• C. 0.654$^\circ$C
• D. -0.654$^\circ$C

Answer 1

Answer: (D)

-0.654$^\circ$C

Answer 2

$\Delta T_b = 100.18 - 100 = 0.18$
$\frac{\Delta T_b}{\Delta T_f} = \frac{K_bm}{K_fm} = \frac{K_b}{K_f}$
$\frac{0.18}{\Delta T_f} = \frac{0.512}{1.86}$
$\Delta T_f = \frac{0.18 \times 1.86}{0.512} = 0.654$
$T_f = (0 - 0.654) ^\circ C = - 0.654^\circ C$